Clearly, such result can be viewed as a generalization of the boundedness by initial energy proposed in [1]}.
It also indicates that the original energy indeed decays w.r.t. time in some small neighborhood at \(t=0\) .
However, it is still unknown if this holds true in longer time.
The construction of upper bound for TFAC equation can be generalized to the time-fractional Cahn–Hilliard (TFCH) equation.
Furthermore, on the discrete level, similar decreasing discrete upper bounds can be obtained for the L1-type and L2-type schemes of the TFAC equation.
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